The relative standard deviation for the set of data obtained by the student is 0.470%
The formula for calculating the relative standard deviation is given below as:
Relative standard deviation (RSD) = (S * 100)/x
where S stands for the standard deviation and x is the mean of the data set.
The following are the steps to calculate to determine the relative standard deviation using the given formula:
Step 1: Calculate the mean of the numbers in the data set.
mean, x = sum of numbers / number of numbers
(40.220 + 40.654 + 40.314 + 40.165 + 40.554)/5
mean = 40.381 g/mol
Step 2: Subtract the mean from each number in the data to determine the deviation for each number and then square the deviations.
(40.220 - 40.381)² = 0.0259
(40.654 - 40.381)² = 0.0745
(40.314 - 40.381)² = 0.00449
(40.165 - 40.381)² = 0.0466
(40.554 -40.381)² = 0.0299
Step 3: Sum the squared deviations.
0.0259 + 0.0745 + 0.00449 + 0.0466 + 0.0299 = 0.181
Step 4: Determine the variance by dividing the sum of the squared deviations by the total number of values.
Variance = 0.181/5 = 0.0362
Step 6: Determine the standard deviation of the data by taking square root of the variance.
Standard deviation, S = √0.0362 = 0.190
Step 7: Determine the relative standard deviation by inserting the values in the formula, (RSD) = (S * 100)/x
RSD = (0.190 * 100)/40.381
RSD = 0.470%
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